Know the Fundamental Theorem of Algebra and verify it for quadratic polynomials.
Verify whether a given real or complex number is a root of a quadratic by substitution
Problem
Use substitution to determine whether \(2\) is a root of \(x^2-5x+6\).
Big Picture
What this problem is really about
A candidate is a root exactly when direct substitution makes the polynomial zero. We’ll replace every occurrence of the variable, preserve the signed coefficient, evaluate powers and products before combining terms, and use a factorization check to confirm the conclusion.
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